The backward shift on spaces of analytic functions

解析函数空间的后移

• 批准号: 0098214
• 负责人: William Ross
• 金额: $ 7.55万
• 依托单位: University of Richmond
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2004-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0098214&HistoricalAwards=false
• 关键词: backward; shift; spaces; analytic; functions

In this project, the PI plans to investigate the `continuation' properties of the invariant subspaces of the backward shift operator on various spaces of analytic functions on the unit disk. In 1970, Douglas, Shapiro, and Shields showed that functions belonging to these invariant subspaces of the Hardy space posses special continuation properties to the exterior disk. In more recent investigations, this idea of `continuation' has been shown to be ubiquitous in that it appears to take place, in one form or another, in many other settings belong the Hardy space case. This proposal plans to get at the heart of the nature of these continuations and why they occur in the first place. This project falls under the broad heading of the field of mathematical analysis which, besides its beauty and elegance, makes many connections and has its roots in problems connected with physics and engineering. In fact, the concept of `continuation' properties of analytic functions has been recently studied by the engineer S. Darlington who connected these `continuations' to properties of electrical circuit design.

在这个项目中，PI计划研究单位圆盘上各种解析函数空间上的后移算子的不变子空间的“连续”性质。 在1970年，道格拉斯，夏皮罗和希尔兹表明，职能属于这些不变子空间的哈代空间的特殊延续性质的外部磁盘。在最近的研究中，这种“延续”的观念已被证明是普遍存在的，因为它似乎以这样或那样的形式发生在属于哈代空间情形的许多其他环境中。这个提议计划得到这些延续的本质的核心，以及为什么它们首先发生。这个项目福尔斯属于广泛的标题领域的数学分析，除了其美丽和优雅，使许多连接，并有其根源的问题与物理和工程。事实上，解析函数的“连续”性质的概念最近已经由工程师S.达林顿将这些“延续”与电路设计的属性联系起来。